code: def _lie_group_remove(coords):
      r"""
      This function is strictly meant for internal use by the Lie group ODE solving
      method. It replaces arbitrary functions returned by pdsolve as follows:
  
      1] If coords is an arbitrary function, then its argument is returned.
      2] An arbitrary function in an Add object is replaced by zero.
      3] An arbitrary function in a Mul object is replaced by one.
      4] If there is no arbitrary function coords is returned unchanged.
  
      Examples
      ========
  
      >>> from sympy.solvers.ode.lie_group import _lie_group_remove
      >>> from sympy import Function
      >>> from sympy.abc import x, y
      >>> F = Function("F")
      >>> eq = x**2*y
      >>> _lie_group_remove(eq)
      x**2*y
      >>> eq = F(x**2*y)
      >>> _lie_group_remove(eq)
      x**2*y
      >>> eq = x*y**2 + F(x**3)
      >>> _lie_group_remove(eq)
      x*y**2
      >>> eq = (F(x**3) + y)*x**4
      >>> _lie_group_remove(eq)
      x**4*y
  
      """
      if isinstance(coords, AppliedUndef):
          return coords.args[0]
      elif coords.is_Add:
          subfunc = coords.atoms(AppliedUndef)
          if subfunc:
              for func in subfunc:
                  coords = coords.subs(func, 0)
          return coords
      elif coords.is_Pow:
          base, expr = coords.as_base_exp()
          base = _lie_group_remove(base)
          expr = _lie_group_remove(expr)
          return base**expr
      elif coords.is_Mul:
          mulargs = []
          coordargs = coords.args
          for arg in coordargs:
              if not isinstance(coords, AppliedUndef):
                  mulargs.append(_lie_group_remove(arg))
          return Mul(*mulargs)
      return coords
  
imports: from itertools import islice
  from sympy.core import Add, S, Mul, Pow
  from sympy.core.exprtools import factor_terms
  from sympy.core.function import Function, AppliedUndef, expand
  from sympy.core.relational import Equality, Eq
  from sympy.core.symbol import Symbol, Wild, Dummy, symbols
  from sympy.functions import exp, log
  from sympy.integrals.integrals import integrate
  from sympy.polys import Poly
  from sympy.polys.polytools import cancel, div
  from sympy.simplify import collect, powsimp, separatevars, simplify
  from sympy.solvers import solve
  from sympy.solvers.pde import pdsolve
  from sympy.utilities import numbered_symbols
  from sympy.solvers.deutils import _preprocess, ode_order
  from .ode import checkinfsol
label_desc: Use image node_id 13 for calling a global function with example usage: _lie_group_remove(coords) and returns: coords, coords, coords, unknown, Mul